Appropriate sample size for unusual "populations"

#1
There seems to be a lot of literature about determining sample size based on population, margin of error and confidence level. This seems difficult to apply to surveys where the "population" consists of large institutions. For example, say it's a survey on investment allocation by public pension funds. The population of such pension funds might be 1000, however the top 50 might be bigger than the next 950. Moreover, most pension funds might be unwilling to participate in surveys, making the accessible population much smaller. In such situations, how do you arrive at a sample size that equates with a credible survey?
 

hlsmith

Not a robit
#3
Your concern seems to be with potential selection bias in the face of a nonrandom sample. If you know characteristics of the population, you my be able to weight you sample to get a better representation.